A method for measuring and calculating water flow inertia time constant of hydroelectric generating set

Abstract

This invention provides a method for the actual calculation of the inertial time constant of water flow in a hydropower unit. It defines a time-invariant inertial time constant based on rated operating parameters; establishes a rigid water hammer transient transfer function that includes the effects of pipeline hydraulic losses and the inertial time constant, thus avoiding the difficulties in measuring large-diameter flow rates in hydropower stations; establishes a transfer function model between the guide vane opening increment and the volute pressure increment based on the rigid water hammer transient transfer function; and establishes a calculation formula for the inertial time constant based on the measured transient data of the guide vane opening increment and the volute pressure increment, using the transfer function model. By performing tests and calculations near rated operating conditions, this method avoids the difficulty in calculating the overflow coefficient due to guide vane opening deviation, and solves the measurement difficulties caused by the fact that the influence of the inertial time constant only exists in the transient process and disappears in steady state.

Description

Technical Field

[0001] This invention relates to the field of hydro turbine parameter calculation technology, and in particular to a method for the actual calculation of the inertial time constant of water flow in a hydro-generator unit. Background Technology

[0002] The inertial time coefficient of pipeline water flow is a core parameter in hydraulic transient calculations and a key parameter in the stability analysis of hydropower units and the optimization of governor control strategies. Initially, in the derivation of pipeline hydraulic transients, a relative value form of the hydraulic system transient transfer function model was established using the initial operating head and flow rate as base values, and the inertial time coefficient of the water flow was defined. The transient state of the hydraulic system, together with the turbine, constitutes the transient calculation model of the turbine. Since linearized models are mainly applied to small disturbances with amplitudes less than 10%, both the hydraulic system and turbine models use the initial operating conditions as the base value to define relative value systems, thus avoiding large calculation errors. In power system applications, to simplify the calculation of the transfer coefficient, values ​​near the rated operating condition are directly given as constant values, also known as the ideal turbine model. It is precisely due to this application scenario that the water flow inertia time coefficient... It has also been gradually misunderstood as the "constant" of water flow inertia time.

[0003] To systematically study the characteristics of the transient process of a hydroelectric generator, the turbine model needs to be connected to the generator per-unit system for analysis. It was found that the ideal turbine model exhibits significant errors in turbine power calculations after deviating from the rated operating point. Furthermore, the ideal turbine model only contains… Parameters, discovered naturally It varies depending on the initial operating conditions. Therefore, in the PSD-BPA software of the China Electric Power Research Institute... A correction factor, to be determined, has been added before the coefficient. In engineering practice, using the turbine power transient curve under guide vane step disturbance as a benchmark, and assuming the simulation curve matches the measured curve, the simulation-given value is used. Approximate as The actual values ​​were obtained one by one under different load conditions. Correction value. In reality, the field tests were only conducted at a specific water head; different water heads... This will also produce corresponding changes. This type of flow inertia time coefficient, defined with the initial operating conditions as the baseline, will... Its application is extremely inconvenient.

[0004] On the other hand, the influence of the flow inertia time coefficient is mainly during the hydraulic transient process; its influence disappears after entering the steady state. It can only be calculated and extracted from transient process data. Furthermore, the large diameter of the water intake system in hydropower stations makes flow measurement difficult. Therefore, There has always been a lack of simple and feasible engineering methods for experimental testing. Summary of the Invention

[0005] In view of this, the present invention proposes a method for the actual calculation of the inertial time constant of water flow in a hydropower unit, thereby solving the problems mentioned in the background art.

[0006] The technical solution of this invention is implemented as follows:

[0007] A method for the experimental calculation of the inertial time constant of water flow in a hydroelectric generator unit includes the following steps:

[0008] Step S1: Define the time constant of water flow inertia that does not change with time based on the rated operating parameters. ;

[0009] Step S2: Establish a rigid water hammer transient transfer function that includes the effects of pipeline hydraulic losses and the inertial time constant of the water flow;

[0010] Step S3: Establish a transfer function model between the guide vane opening increment and the volute water pressure increment based on the rigid water hammer hydraulic transient transfer function;

[0011] Step S4: Establish a transfer function model between the guide vane opening increment and the volute water pressure increment, and calculate the flow inertial time constant based on the measured transient data of the guide vane opening increment and the volute water pressure increment. The calculation formula.

[0012] Preferably, the specific steps of step S1 are as follows:

[0013] The expression for the acceleration of the water column caused by the change in water head at the inlet of the turbine casing, according to Newton's second law, is:

[0014] ;

[0015] in For the length of the pipe, For the pipe area, For water density, It is the acceleration due to gravity. For water flow velocity, For water head;

[0016] Obtain initial operating flow and initial working head ,use Dividing by the expression for water column acceleration yields the expression for the relative value:

[0017] ;

[0018] in For traffic;

[0019] Define the inertial time constant of water flow for:

[0020] = .

[0021] Preferably, it incorporates the inertial time constant of the water flow. Transforming the relative value expression yields the rigid water hammer differential equation for the pipe:

[0022] ;

[0023] in Based on the initial operating flow rate and initial working head It is a relative value of the base value.

[0024] Preferably, the specific steps of step S2 are as follows:

[0025] The rigid water hammer differential equations for a pipe satisfy the Laplace transform zero initial condition and can be rewritten in the form of a hydraulic system transfer function:

[0026] ;

[0027] in For the increase of water head, To increase traffic, For the Laplace operator.

[0028] Preferably, after obtaining the transfer function, the friction loss head is added to rewrite the hydraulic system transfer function and obtain the rigid water hammer transient transfer function as follows:

[0029] ;

[0030] in This is the pipeline friction loss coefficient in a relative sense.

[0031] Preferably, step S3 includes the following specific steps:

[0032] The turbine flow rate can be described using the orifice outflow formula:

[0033] ;

[0034] in It is the flow coefficient. For guide vane opening, It is the turbine head;

[0035] At the initial operating point, a Taylor expansion of the orifice outflow formula is performed, neglecting second-order and higher-order terms. , As the base value, it can be written in relative value form as:

[0036] ;

[0037] in It is the relative value of the guide vane opening and the turbine head at the initial operating point. This represents the increment of the guide vane opening.

[0038] Relative value of guide vane opening Defined using the following formula:

[0039] ;

[0040] in This refers to the opening of the governor guide vanes under rated head and rated flow. Based on the governor opening base value The relative value as the baseline;

[0041] definition use Representing the initial relative value of the guide vane opening, the orifice outflow formula is transformed into a linearized equation:

[0042] .

[0043] Preferably, step S3 further includes the following steps:

[0044] Multiplying both sides of the linearized equation by the hydraulic system transfer function yields:

[0045] ;

[0046] in This is the flow correction factor;

[0047] Substituting the relative value form of the orifice outflow formula into the above equation, we get:

[0048] ;

[0049] make , , ,Will , , Substituting into the above equation, we obtain the transfer function model between the guide vane opening increment and the volute water pressure increment:

[0050] .

[0051] Preferably, step S4 includes the following specific steps:

[0052] In increment , Under the condition of zero initialization satisfying the Laplace transform, the transfer function model between the guide vane opening increment and the volute water pressure increment is rewritten in differential equation form:

[0053] .

[0054] Preferably, step S4 further includes the following steps:

[0055] Integrating the differential equation yields the flow inertial time constant calculated based on measured transient data of water pressure in the volute from the guide vane opening increment. The calculation formula is as follows:

[0056] ;

[0057] The integration time interval [ , [This refers to the set transient calculation time length.] It is the time interval for discrete calculations.

[0058] Compared with the prior art, the beneficial effects of the present invention are:

[0059] The present invention provides a method for the actual calculation of the inertial time constant of water flow in a hydropower unit, which belongs to the field of turbine stability analysis and control design technology. After defining the inertial time coefficient of water flow with rated head and flow rate as base values, a rigid water hammer hydraulic transient transfer function including pipeline hydraulic loss is introduced to establish a refined model of the transfer function from guide vane opening to volute water pressure, thus avoiding the difficulty of measuring the flow rate of large-diameter pipes in hydropower stations.

[0060] A method for calculating the inertial time constant of water flow using easily measurable guide vane opening and transient process data of water pressure at the volute inlet is proposed. The test calculation is carried out near the rated operating conditions, avoiding the problem of difficulty in calculating the flow coefficient when the guide vane opening deviates from the rated flow coefficient.

[0061] This study solves the problem that the influence of the inertial time constant of water flow only exists in the transient process and disappears under steady-state conditions, which makes it difficult to measure the inertial time constant of water flow in hydropower stations. Attached Figure Description

[0062] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. In the following description, the expression "some embodiments" refers to a subset of all possible embodiments; however, it should be understood that "some embodiments" can be the same subset or different subsets of all possible embodiments and can be combined with each other without conflict.

[0063] In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention can be practiced without one or more of these details. In other instances, certain technical features well-known in the art have not been described in order to avoid obscuring the invention.

[0064] It should be understood that the present invention can be embodied in various forms and should not be construed as being limited to the embodiments set forth herein. Rather, providing these embodiments will make the disclosure thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Furthermore, the terminology used herein is intended only to describe particular embodiments and is not intended to limit the invention. When used herein, the singular forms “a,” “an,” and “the” are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the terms “compose” and / or “comprising,” when used in this specification, identify the presence of the stated features, integers, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups. When used herein, the term “and / or” includes any and all combinations of the associated listed items.

[0065] It should also be noted that when an element is referred to as being "fixed to" another element, it can be directly attached to the other element or there may be an intervening element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or there may be an intervening element. The terms "vertical," "horizontal," "inner," "outer," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible implementation.

[0066] To fully understand this invention, a detailed structure will be presented in the following description to illustrate the technical solution proposed by this invention. Optional embodiments of the invention are described in detail below; however, in addition to these detailed descriptions, the invention may have other embodiments.

[0067] Figure 1 This is a flowchart illustrating a method for the actual calculation of the inertial time constant of a hydroelectric generator set according to the present invention.

[0068] Figure 2 The measured data diagram of hydropower station 1 is selected for the actual calculation method of the inertial time constant of water flow in a hydropower unit according to the present invention;

[0069] Figure 3 This is a schematic diagram of filtered measured data from hydropower station 2, selected for the method of calculating the inertial time constant of water flow in a hydropower unit according to the present invention. Detailed Implementation

[0070] To better understand the technical content of this invention, a specific embodiment is provided below, and the invention will be further described in conjunction with the accompanying drawings.

[0071] See Figure 1 The present invention provides a method for the experimental calculation of the inertial time constant of water flow in a hydroelectric generator, comprising the following steps:

[0072] Step S1: Define the time constant of water flow inertia that does not change with time based on the rated operating parameters. ;

[0073] The specific steps are as follows:

[0074] The expression for the acceleration of the water column caused by the change in water head at the inlet of the turbine casing, according to Newton's second law, is:

[0075] ;

[0076] in For the length of the pipe, For the pipe area, For water density, It is the acceleration due to gravity. For water flow velocity, For water head;

[0077] Obtain initial operating flow and initial working head ,use Dividing by the expression for water column acceleration yields the expression for the relative value:

[0078] ;

[0079] in For traffic;

[0080] Define the inertial time constant of water flow for:

[0081] = .

[0082] Preferably, it incorporates the inertial time constant of the water flow. Transforming the relative value expression yields the rigid water hammer differential equation for the pipe:

[0083] ;

[0084] in Based on the initial operating flow rate and initial working head It is a relative value of the base value.

[0085] The above definitions are based on rated operating head and flow rate. For a hydropower station with a fixed layout, the pipeline length and cross-sectional area remain unchanged. It is a constant value that is only related to the physical parameters of the pipeline, defined by the rated operating condition parameters, and does not change with the operating conditions of the group.

[0086] Step S2: Establish a rigid water hammer transient transfer function that includes the effects of pipeline hydraulic losses and the inertial time constant of the water flow;

[0087] The specific steps are as follows:

[0088] The differential equations for rigid water hammer in a pipe are incremental differential equations that satisfy the Laplace transform zero initial condition and can be rewritten in the form of hydraulic system transfer functions:

[0089] ;

[0090] in For the increase of water head, To increase traffic, For the Laplace operator.

[0091] The hydraulic system transfer function described above neglects the head loss due to pipe friction. One way to handle this is to directly add the head loss after obtaining the transfer function, which yields higher calculation accuracy. Therefore, the hydraulic system transfer function can be rewritten to obtain the rigid water hammer transient transfer function as follows:

[0092] ;

[0093] in The pipeline friction loss coefficient is a relative value and is a structural parameter of the hydraulic system that does not change with operating conditions.

[0094] Hydropower station water intake pipes have large diameters, making flow measurement difficult. This invention proposes an indirect calculation method using the easily measurable turbine guide vane opening.

[0095] Step S3: Establish a transfer function model between the guide vane opening increment and the volute water pressure increment based on the rigid water hammer hydraulic transient transfer function;

[0096] The specific steps include:

[0097] The turbine flow rate can be described using the orifice outflow formula:

[0098] ;

[0099] in It is the flow coefficient. For guide vane opening, It is the turbine head;

[0100] At the initial operating point (subscript 0), a Taylor expansion of the orifice outflow formula is performed, ignoring second-order and higher-order terms. , As the base value, it can be written in relative value form as:

[0101] ;

[0102] in It is the relative value of the guide vane opening and the turbine head at the initial operating point. This represents the increment of the guide vane opening.

[0103] The guide vane opening of the governor in a hydropower station is a relative opening. The base value for this opening is sometimes unclear. To avoid this problem, the following method is used to define it:

[0104] ;

[0105] in This refers to the opening of the governor guide vanes under rated head and rated flow. Based on the governor opening base value The relative value is used as a benchmark; in the field testing of hydropower stations, the governor opening data is directly used for calculation, for ease of application. Still using Representing the initial relative value of the guide vane opening, the orifice outflow formula is transformed into a linearized equation:

[0106] .

[0107] The flow coefficient in the orifice outflow formula is similar to the turbine efficiency, which varies with the opening degree (power). This increases the complexity of the calculation. In this invention, the rated operating condition parameter is used as the base value. The K value changes little near the rated operating condition and is approximately a constant, which will not produce a large calculation error. Therefore, the actual measurement calculation condition specified in this invention is to use the measured data near the rated operating condition point for calculation.

[0108] water turbine head This refers to the pressure difference between the turbine inlet and outlet. The turbine inlet pressure is approximately equal to the spiral casing pressure or the pressure at the end of the steel pipe, while the runner outlet pressure is equal to the draft tube inlet pressure. With minimal guide vane adjustment, the draft tube inlet pressure fluctuation is also small, resulting in a small increase in turbine head. This can be approximated as the increase in volute pressure, and its physical meaning is consistent with the increase in transient hydraulic pressure in a pipeline. The increase in volute inlet pressure can be used. replace.

[0109] Multiplying both sides of the linearized equation by the hydraulic system transfer function yields:

[0110] ;

[0111] in This is the flow correction factor, calculated near the rated operating conditions, and approximately taken as 1;

[0112] In the transient transfer function of rigid water hammer For ease of processing, we take an approximation. Substituting the relative value form of the orifice outflow formula into the above equation, we get:

[0113] ;

[0114] make , , ,Will , , Substituting into the above equation, we obtain the transfer function model between the guide vane opening increment and the volute water pressure increment:

[0115] .

[0116] Step S4: Establish a transfer function model between the guide vane opening increment and the volute water pressure increment, and calculate the flow inertial time constant based on the measured transient data of the guide vane opening increment and the volute water pressure increment. The calculation formula;

[0117] The specific steps include:

[0118] In increment , Under the condition of zero initialization satisfying the Laplace transform, the transfer function model between the guide vane opening increment and the volute water pressure increment is rewritten in differential equation form:

[0119] .

[0120] Integrating the above differential equation yields the flow inertial time constant calculated based on the measured transient data of water pressure in the volute from the guide vane opening increment. The calculation formula is as follows:

[0121] ;

[0122] The integration time interval [ , [This refers to the set transient calculation time length.] It is the time interval for discrete calculations.

[0123] Linearization is performed near the initial operating point, with variables containing Δ using the initial operating point as the reference point. , .

[0124] The method of this invention is verified below by actual measurements at a hydropower station:

[0125] Parameters X, B, and C need to be calculated in advance, which involves the generator unit. , , and initial operating parameters , .

[0126] At any water head and rated head When the rated output is given, the efficiencies of the two are approximately equal. Therefore, at the rated output point, approximately: , Calculate using the following formula:

[0127] ;

[0128] Steady-state volute pressure satisfies , It is the static head at the inlet of the volute, that is, the elevation difference between the upstream water level and the inlet of the volute. Two data points close to the rated power are selected. , Calculate according to the following formula:

[0129] ;

[0130] (1) The measured data of hydropower station 1 were filtered using a recursive multi-point continuous averaging method to reduce data fluctuation errors. The first segment of data (30s-100s) was selected for filtering, such as... Figure 2 As shown:

[0131] Calculations can be performed to obtain the turbine head. , =0.0250, The inertial time constant of the water flow is calculated based on the measured transient data of the guide vane opening increment to the volute water pressure. The calculation formula is used to obtain , The theoretical value is 3.42, with an error of 4.6554%.

[0132] The filtered data from the measured data of hydropower station 2 is as follows: Figure 3 As shown:

[0133] The calculation was performed using data from the first disturbance period of 8-15 seconds:

[0134] Among them, the turbine head , , Calculated , The theoretical value is 1.887, with an error of -3.7443%.

[0135] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for the measured calculation of the inertial time constant of water flow in a hydroelectric generator unit, characterized in that, Includes the following steps: Step S1: Define the time constant of water flow inertia that does not change with time based on the rated operating parameters. ; Step S2: Establish a rigid water hammer transient transfer function that includes the effects of pipeline hydraulic losses and the inertial time constant of the water flow; Step S3: Establish a transfer function model between the guide vane opening increment and the volute water pressure increment based on the rigid water hammer hydraulic transient transfer function; Step S4: Establish a transfer function model between the guide vane opening increment and the volute water pressure increment, and calculate the flow inertial time constant based on the measured transient data of the guide vane opening increment and the volute water pressure increment. The calculation formula; The expression for the acceleration of the water column caused by the change in water head at the inlet of the turbine casing, according to Newton's second law, is: ； in For the length of the pipe, For the pipe area, For water density, It is the acceleration due to gravity. For water flow velocity, For water head; Obtain initial operating flow and initial working head ,use Dividing by the expression for water column acceleration yields the expression for the relative value: ； in For traffic; Define the inertial time constant of water flow for: = ； Combining the inertial time constant of water flow Transforming the relative value expression yields the rigid water hammer differential equation for the pipe: ； in Based on the initial operating flow rate and initial working head The relative value of the base value; The specific steps of step S2 are as follows: The rigid water hammer differential equations for a pipe satisfy the Laplace transform zero initial condition and can be rewritten in the form of a hydraulic system transfer function: ； in For the increase of water head, To increase traffic, For the Laplace operator; After obtaining the transfer function, adding the frictional head loss, the hydraulic system transfer function is rewritten, and the rigid water hammer transient transfer function is obtained as follows: ； in This refers to the pipeline friction loss coefficient in a relative sense. The specific steps of step S3 include: The turbine flow rate can be described using the orifice outflow formula: ； in It is the flow coefficient. For guide vane opening, It is the turbine head; At the initial operating point, a Taylor expansion of the orifice outflow formula is performed, neglecting second-order and higher-order terms. , As the base value, it can be written in relative value form as: ； in It is the relative value of the guide vane opening and the turbine head at the initial operating point. This represents the increment of the guide vane opening. Relative value of guide vane opening Defined using the following formula: ； in This refers to the guide vane opening of the speed governor under rated head and rated flow. Based on the governor opening base value The relative value as the baseline; definition use Representing the initial relative value of the guide vane opening, the orifice outflow formula is transformed into a linearized equation: ； The specific steps of step S3 also include: Multiplying both sides of the linearized equation by the hydraulic system transfer function yields: ； in This is the flow correction factor; Substituting the relative value form of the orifice outflow formula into the above equation, we get: ； make , , ,Will , , Substituting into the above equation, we obtain the transfer function model between the guide vane opening increment and the volute water pressure increment: ； The specific steps of step S4 include: In increment , Under the condition of zero initialization satisfying the Laplace transform, the transfer function model between the guide vane opening increment and the volute water pressure increment is rewritten in differential equation form: ； The specific steps of step S4 also include: Integrating the differential equation yields the flow inertial time constant calculated based on measured transient data of water pressure in the volute from the guide vane opening increment. The calculation formula is as follows: ； The integration time interval [ , [This refers to the set transient calculation time length.] It is the time interval for discrete calculations.

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